Problem of finding General value

Question

The general value $e^i$ is given by___

$$e^i=e^{\cos(2n\pi+\pi/2)+i\sin(2n\pi+\pi/2)}=e^{e^{2n\pi+\pi/2}}, \quad \forall n\in I$$

Is it right? But here, I need answer $e^{-(2n\pi+\pi/2)}, \forall n\in I$

How to get that answer?